The advancement of technology has led to an increasing demand for efficient and reliable data transmission and storage systems. This demand has led to the creation of new methods of data encryption for data storage and data transmission over physical channels. In addition, a major concern of the designers of such systems has been the controlling of errors so that reliable reproduction of data can be obtained.
Filter banks and wavelet transforms have established themselves as powerful tools in the analysis of signals and images when these objects are viewed as sequences over real or complex fields. The extension of the wavelet transform to the situation in which the complex field is replaced with a finite field is of particular interest since wavelets and filter banks over finite fields have potential application in cryptography and the theory of error correction codes.